三维齐次空间中的多谐曲面

IF 0.5 4区数学 Q3 MATHEMATICS Manuscripta Mathematica Pub Date : 2023-11-13 DOI:10.1007/s00229-023-01520-4

S. Montaldo, C. Oniciuc, A. Ratto

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引用次数: 1

摘要

摘要本文第一部分对三维齐次空间(bianchi - cartan - vrancanu空间，简称bcv空间)中的固有三谐等参曲面进行了分类。我们还将证明三谐波霍普夫圆柱必然是CMC。在最后一节中，我们将确定bcv空间中CMC r -谐波Hopf圆柱的完整分类，$$r \ge 3$$ r≥3。这个结果保证了在合适的r值下，在bcv空间中存在大量的r -调和曲面的新实例。

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Polyharmonic surfaces in 3-dimensional homogeneous spaces

Abstract In the first part of this paper we shall classify proper triharmonic isoparametric surfaces in 3-dimensional homogeneous spaces (Bianchi-Cartan-Vranceanu spaces, shortly BCV-spaces). We shall also prove that triharmonic Hopf cylinders are necessarily CMC. In the last section we shall determine a complete classification of CMC r -harmonic Hopf cylinders in BCV-spaces, $$r \ge 3$$ r ≥ 3 . This result ensures the existence, for suitable values of r , of an ample family of new examples of r -harmonic surfaces in BCV-spaces.

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来源期刊

Manuscripta Mathematica 数学-数学

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： manuscripta mathematica was founded in 1969 to provide a forum for the rapid communication of advances in mathematical research. Edited by an international board whose members represent a wide spectrum of research interests, manuscripta mathematica is now recognized as a leading source of information on the latest mathematical results.

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